Near-optimal low-complexity decoding of space-time codes for fixed wireless applications

ABSTRACT

An improved multi-antenna receiver is realized for detecting signals transmitted by a multi-antenna transmitter by summing signals received at the plurality of receiver antennas after multiplying each by a respective constant. The summed signal is applied to a maximum likelihood detector. The respective constants, λ j , where j is an index designating a particular receiver antenna, are determined by evaluating the largest eigenvalue of the matrix ΛA(Λ*) T , where Λ is a vector containing the values λ j , and A is a matrix containing elements α ij , which is the transfer function between the i th  transmitter antenna to the j th  receiver antenna. The α ij  terms are determined in the receiver in conventional ways.

REFERENCE TO RELATED APPLICATIONS

[0001] This application claims the benefit of U.S. ProvisionalApplication No. 60/068,613, filed Dec. 23, 1997.

BACKGROUND OF THE INVENTION

[0002] This invention relates to wireless systems and, moreparticularly, to systems having more than one antenna at the receiverand at the transmitter.

[0003] Physical constraints as well as narrow bandwidth, co-channelinterference, adjacent channel interference, propagation loss andmulti-path fading limit the capacity of cellular systems. These aresevere impairments, which liken the wireless channel to a narrow pipethat impedes the flow of data. Nevertheless, interest in providing highspeed wireless data services is rapidly increasing. Current cellularstandards such as IS-136 can only provide data rates up to 9.6 kbps,using 30 kHz narrowband channels. In order to provide wideband services,such as multimedia, video conferencing, simultaneous voice and data,etc., it is desirable to have data rates in the range of 64-144 kbps.

[0004] Transmission schemes for multiple antenna systems may be part ofa solution to the problem of the currently available low data rates.Such schemes were first proposed in papers by Wittneben, and by Seshadriand Winters, where the problem was addressed in the context of signalprocessing.

[0005] One prior art arrangement having a single transmitter antenna andmultiple receiver antennas is shown in FIG. 1. Each of the receiverantennas receives the transmitted signal via a slightly differentchannel, where each channel i is characterized by transfer functionα_(i). Using an approach known as “Maximum Ratio Combining”, the priorart approach to detection contemplates multiplying each received signalthat had been influenced by α_(i) by the complex conjugate signal,α_(i)*, summed, and then processed.

[0006] In a co-pending application titled “Method and Apparatus for DataTransmission Using Space-Time Codes and Multiple Transmit Antennas”,filed on May 6, 1997, bearing the Ser. No. 08/847,635, and assigned tothe assignee of this invention, a coding perspective was adopted topropose space-time coding using multiple transmit and receive antennas.Space-time coding integrates channel coding, modulation, and multipletransmit antennas to achieve higher data rates, while simultaneouslyproviding diversity that combats fading. It may be demonstrated thatadding channel coding provides significant gains over the schemes ofWittneben and Seshadri and Winters. In said co-pending application,space-time codes were designed for transmission using 2-4 transmitantennas. These codes perform extremely well in slowly varying fadingenvironments (such as indoor transmission media). The codes have userbandwidth efficiencies of up to 4 bits/sec/Hz which are about 3-4 timesthe efficiency of current systems. Indeed, it can be shown that thedesigned codes are optimal in terms of the trade-off between diversityadvantage, transmission rate, decoding complexity and constellationsize.

[0007] It can also be shown that as the number of antennas is increased,the gain increases in a manner that is not unlike a multi-elementantenna that is tuned to, say, a particular direction Unfortunately,however, when maximum likelihood detection is employed at the receiver,the decoding complexity increases when the number of transmit andreceive antennas is increased. It would be obviously advantageous toallow a slightly sub-optimal detection approach that substantiallyreduces the receiver's computation burden.

SUMMARY

[0008] Such an approach is achieved with a receiver arrangement wheresignals received at a plurality of antennas are each multiplied by arespective constant and then summed prior to being applied to a maximumlikelihood detector. The respective constants, λ_(l), where j is anindex designating a particular receiver antenna, are derived from aprocessor that determines the largest eigenvalue of the matrix ΛA(Λ*)T,where Λ is a vector containing the values λ_(j), and A is a matrixcontaining elements α_(ij), which is the transfer function between thei^(th) transmitter antenna to the j^(th) receiver antenna. The α_(ij)terms are determined in the receiver in conventional ways.

BRIEF DESCRIPTION OF THE DRAWING

[0009]FIG. 1 presents a block diagram of Maximal Ratio Combiningdetection; and

[0010]FIG. 2 presents a block diagram of an arrangement including atransmitter having a plurality of antennas, and a receiver having aplurality of antennas coupled to an efficient detection structure.

DETAILED DESCRIPTION

[0011]FIG. 1 presents a block diagram of a receiver in accord with theprinciples of this invention. It includes a transmitter 10 that has an nplurality of transmitting antenna 1, 2, 3, 4, and a receiver 20 that hasan m plurality of receiver antennas 21, 22, 23, 24. The signals receivedby the receiver's antennas are multiplied in elements 25, 26, 27, and28, and summed in adder 30. More specifically, the received signal ofantenna j is multiplied by a value, λ_(j), and summed. The collection offactors λ_(j) can be viewed as a vector A. The outputs of the receiverantennas are also applied to processor 40 which, employing conventionaltechniques, determines the transfer functions α_(ij) for i=1, 2, 3, . .. , n and j=1, 2, 3, . . . , m. These transfer functions can beevaluated, for example, through the use of training sequences that aresent by the different transmitter antennas, one antenna at a time.

[0012] The evaluated α_(ij) signals of processor 40 are applied toprocessor 45 in FIG. 1 where the multiplier signals λ_(j), ,j=1, 2, 3, .. . , m are computed. Processor 45 also evaluates a set of combinedtransfer function values γ_(i), i=1, 2, 3, . . . , n (which aredescribed in more detail below). Signals γ_(i) of processor 45 and theoutput signal of adder 30 are applied to detector 50 which detects thetransmitted symbols in accordance with calculations disclosed below.

[0013] It is assumed that the symbols transmitted by the antennas oftransmitter 10 have been encoded in blocks of L time frames, and thatfading is constant within a frame. A codeword comprises all of thesymbols transmitted within a frame, and it corresponds, therefore, to

c₁ ¹c₁ ²c₁ ³ . . . c₁ ⁴c₂ ¹c² ²c₂ ³ . . . c₂ ⁴c₃ ¹c₃ ²c₃ ³ . . . c₃ ⁴ .. . c_(m) ¹c_(m) ²c_(m) ³ . . . c_(m) ⁴,  (1)

[0014] where the superscript designates the transmitter's antennas andthe subscript designates the time of transmission (or position within aframe).

[0015] From the standpoint of a single antenna, e.g., antenna 1, thesignal that is received at antenna 1 in response to a transmitted symbolc₁ ¹ at time interval t is: $\begin{matrix}\begin{matrix}{R_{i} = {c_{i}^{1}\left( {{a_{11}\lambda_{1}} + {a_{12}\lambda_{2}} + {\alpha_{13}\lambda_{3}} + \ldots + {a_{1m}\lambda_{m}}} \right)}} \\{= {c_{i}^{1}{\sum\limits_{j = 1}^{m}{\lambda_{j}a_{1j}}}}} \\{= {c_{i}^{1}\gamma_{1}}}\end{matrix} & (2)\end{matrix}$

[0016] (when noise is ignored). If each λ_(j) value is set to α*_(ij),(where α*_(ij) is the complex conjugate of α_(ij)) then the receivedsignal would simply be $\begin{matrix}{R_{i} = \left. {c_{i}^{11}\sum\limits_{i = 1}^{m}} \middle| \alpha_{11} \right|^{2}} & (3)\end{matrix}$

[0017] yielding a constructive addition.

[0018] Of course, the values of λ_(j) cannot be set to match α*_(ij) andconcurrently to match the values of α*_(ij) where i≠1; and therein liesthe difficulty.

[0019] When all n of the transmitting antennas are considered, then thereceived signal is $\begin{matrix}{\begin{matrix}{R_{i} = {\sum\limits_{i = 1}^{n}\left( {c_{i}^{i}{\sum\limits_{j = 1}^{m}{\lambda_{j}\alpha_{ij}}}} \right)}} \\{= {\sum\limits_{i = 1}^{n}{c_{i}^{i}\gamma_{i}}}}\end{matrix}\quad} & (4)\end{matrix}$

[0020] In accordance with the present disclosure, the objective is tomaximize $\sum\limits_{i = 1}^{n}\left| \gamma_{i} \right|^{2}$

[0021] because by doing so, signal R₁ contains as much information aboutc₁ ¹, i=1, 2, 3, . . . n as is possible. However, it can be easily shownthat if a matrix A is constructed such that $\begin{matrix}{{A = {\sum\limits_{i = 1}^{n}{\left( \Omega_{i}^{*} \right)^{T}\Omega_{i}}}},} & (5)\end{matrix}$

[0022] where Ω_(i)=(α_(i) ₁, α₁₂, α₁₃ . . . a_(im)), then$\begin{matrix}{{\sum\limits_{i = 1}^{n}\left| \gamma_{i} \right|^{2}} = {\Lambda \quad {{A\left( \Lambda^{*} \right)}^{T}.}}} & (6)\end{matrix}$

[0023] The receiver, thus, has to maximize ΛA(Λ*)^(T), subject to theconstraint ∥Λ∥²=1. The solution to this problem is to choose Λ to be theeigenvector of A which corresponds to the maximum eigenvalue of A.Accordingly, processor 45 develops the matrix A from the values ofα_(ij), finds the eigenvalues of A in a conventional manner, selects themaximum eigenvalue of A, and creates the vector Λ. Once A is known,processor 45 develops signals γ_(i) for 1=1, 2, 3, . . . , n, (where$\gamma_{i} = {\sum\limits_{j = 1}^{m}{\lambda_{j}a_{ij}}}$

[0024] ), and applies them to detector 50. Finally, detector 50minimizes the metric$\sum\limits_{i = 1}^{L}\left| {R_{i} - {\sum\limits_{i = 1}^{n}{\gamma_{i}c_{i}^{i}}}} \right|^{2}$

[0025] from amongst all possible codewords in a conventional manner. Ascan be seen, this approach reduces the complexity of decoding by almosta factor of m.

[0026]FIG. 1 depicts separate multipliers to multiply received signalsby multiplication factors λ_(i), and it depicts separate blocks forelements 30, 40, 45, and 50. It should be understood, however, thatdifferent embodiments are also possible. For example, it is quiteconventional to incorporate all of the above-mentioned elements in asingle special purpose processor, or in a single stored programcontrolled processor (or a small number of processors). Othermodifications and improvements may also be incorporated, withoutdeparting from the spirit and scope of the invention, which is definedin the following claims.

We claim:
 1. A receiver comprising: an n plurality of antennas, where n is greater than one; circuitry for obtaining n signals transmitted from m antennas of a transmitter, where m is greater than one; and processing means for developing a sum signal that corresponds to the addition of said n signals that are each pre-multiplied by a respective factor λ_(i), where i is an index integer specifying that factor λ_(i) multiplies the signal received from antenna i of said n plurality of antennas, developing values for transfer functions α_(i), where i is an index that references said transmitting antennas, and j is an index that references said receiving antennas, developing said λ_(i) factors from said transfer functions, and detecting symbols transmitted by said m transmitter antennas embedded in said sum signal.
 2. The receiver of claim 1 where said factors λ_(j) are related to said transfer functions α_(i).
 3. The receiver of claim 1 where said factors are components of a vector Λ where Λ is an eigenvalue of ΛA(Λ*)^(T), and where A is a matrix containing said elements α_(i).
 4. The receiver of claim 1 where said detecting compares said sum signal to a signal corresponding to symbols c¹ possibly transmitted by transmitting antenna i of said m transmitting antennas multiplied by corresponding factors γ_(i).
 5. The receiver of claim 4 where said corresponding factor γ_(i) is related to said factors λ_(j), for j=1, 2, 3, . . . , m, and to α_(ij).
 6. The receiver of claim 4 where said detecting maximizes the metric $\sum\limits_{i = 1}^{L}\left| {R_{i} - {\sum\limits_{i = 1}^{n}{\gamma_{i}c_{i}^{i}}}} \right|^{2}$

where R_(t) is said sum signal at time interval t within a frame having L time intervals, and c₁ ¹ is the symbol that might have been transmitted over transmitting antenna i at time interval t. 